Problem: Solve for $x$ and $y$ using substitution. ${6x+6y = 6}$ ${x = -6y+11}$
Solution: Since $x$ has already been solved for, substitute $-6y+11$ for $x$ in the first equation. ${6}{(-6y+11)}{+ 6y = 6}$ Simplify and solve for $y$ $-36y+66 + 6y = 6$ $-30y+66 = 6$ $-30y+66{-66} = 6{-66}$ $-30y = -60$ $\dfrac{-30y}{{-30}} = \dfrac{-60}{{-30}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = -6y+11}\thinspace$ to find $x$ ${x = -6}{(2)}{ + 11}$ $x = -12 + 11$ ${x = -1}$ You can also plug ${y = 2}$ into $\thinspace {6x+6y = 6}\thinspace$ and get the same answer for $x$ : ${6x + 6}{(2)}{= 6}$ ${x = -1}$